Abstract
A mobile robot, represented by a point moving along a polygonal line in the plane, has to explore an unknown polygon and return to the starting point. The robot has a sensing area which can be a circle or a square centered at the robot. This area shifts while the robot moves inside the polygon, and at each point of its trajectory the robot “sees” (explores) all points for which the segment between the robot and the point is contained in the polygon and in the sensing area. We focus on two tasks: exploring the entire polygon and exploring only its boundary. We consider several scenarios: both shapes of the sensing area and the Manhattan and the Euclidean metrics.
We focus on two quality benchmarks for exploration performance: optimality (the length of the trajectory of the robot is equal to that of the optimal robot knowing the polygon) and competitiveness (the length of the trajectory of the robot is at most a constant multiple of that of the optimal robot knowing the polygon). Most of our results concern rectilinear polygons. We show that optimal exploration is possible in only one scenario, that of exploring the boundary by a robot with square sensing area, starting at the boundary and using the Manhattan metric. For this case we give an optimal exploration algorithm, and in all other scenarios we prove impossibility of optimal exploration. For competitiveness the situation is more optimistic: we show a competitive exploration algorithm for rectilinear polygons whenever the sensing area is a square, for both tasks, regardless of the metric and of the starting point. Finally, we show a competitive exploration algorithm for arbitrary convex polygons, for both shapes of the sensing area, regardless of the metric and of the starting point.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albers, S., Kursawe, K., Schuierer, S.: Exploring unknown environments with obstacles. Algorithmica 32(1), 123–143 (2002)
Arkin, E.M., Fekete, S.P., Mitchell, J.S.B.: Approximation algorithms for lawn mowing and milling. Comput. Geom. Theory Appl. 17(1-2), 25–50 (2000)
Chin, W., Ntafos, S.: Optimum watchman routes. In: Proc. of Symposium on Computational Geometry (SCG 1986), pp. 24–33 (1986)
Deng, X., Kameda, T., Papadimitriou, C.: How to learn an unknown environment. In: Proc. of Foundations of Computer Science (FOCS ), pp. 298–303 (1991)
Deng, X., Kameda, T., Papadimitriou, C.: How to learn an unknown environment: the rectilinear case. J. ACM 45(2), 215–245 (1998)
Gabriely, Y., Rimon, E.: Spanning-tree based coverage of continuous areas by a mobile robot. In: Int. Conf. of Robotics and Automaton (ICRA 2001), pp. 1927–1933 (2001)
Ghosh, S., Burdick, J., Bhattacharya, A., Sarkar, S.: Online algorithms with discrete visibility - exploring unknown polygonal environments. Robotics & Automation Magazine 15(2), 67–76 (2008)
Hammar, M., Nilsson, B.J., Schuierer, S.: Improved exploration of rectilinear polygons. Nordic J. of Computing 9(1), 32–53 (2002)
Held, M.: On the computational geometry of pocket machining. Springer-Verlag New York, Inc., New York (1991)
Hoffmann, F., Icking, C., Klein, R., Kriegel, K.: The polygon exploration problem. SIAM J. Comput. 31(2), 577–600 (2001)
Icking, C., Kamphans, T., Klein, R., Langetepe, E.: On the competitive complexity of navigation tasks. In: Revised Papers from the International Workshop on Sensor Based Intelligent Robots, London, UK, 2002, pp. 245–258. Springer, London (2002)
Icking, C., Kamphans, T., Klein, R., Langetepe, E.: Exploring simple grid polygons. In: In 11th Internat. Comput. Combin. Conf., pp. 524–533 (2005)
Kleinberg, J.M.: On-line search in a simple polygon. In: Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA 1994), pp. 8–15 (1994)
Moret, B.M.E., Collins, M., Saia, J., Yu, L.: The ice rink problem. In: Proc. of the 1st Workshop on Algorithm Engineering (1997)
Ntafos, S.: Watchman routes under limited visibility. Comput. Geom. Theory Appl. 1(3), 149–170 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Czyzowicz, J., Labourel, A., Pelc, A. (2009). Optimality and Competitiveness of Exploring Polygons by Mobile Robots. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-642-04128-0_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04127-3
Online ISBN: 978-3-642-04128-0
eBook Packages: Computer ScienceComputer Science (R0)